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The Attraction of “Phase Space”, Levi’s Missing Objects

In his usual grasp at the sciences for metaphors Levi has touched on something of interest I think, as I have been reading Stonier’s extremely compelling book Information and the Internal Structure of the universe  (1990), upon which I hope to post soon. In his still vestige symptomatic Lacanianism, Levi uses the “matheme” (the desire to “talk” in the analogy of an algebra) of the crossed out “O” to indicate the “object” that is ever in retreat. In a very nice passage we get a sense of the sense he is trying to make of the idea that objects retreat from their interactions:

At any rate, some differences between Harman’s ontography and my onticology are readily evident in the second paragraph quoted above. With Harman I argue that objects withdraw from other objects, however I arrive at this position for a very different set of reasons. In my view, the withdrawal of objects is the result of the difference between dimensions of objects or Ø and O1. Within the framework of onticology Ø or the matheme for the split or barred object refers to the endo-relational structure of the object. This endo-relational structure consists of a system of attractors defining the phase space of an object or all possible ways in which an object can actualize itself. Attractors are states towards which a system tends, whereas a phase space consists of all possible states a system can occupy. Thus, for example, if you roll a marble down the side of a bowl, the final point at which the marble comes to rest is a fixed point attractor of this system. By contrast, the phase space of this system is all the points the marble can occupy as it rolls up and down the sides of the bowl. I argue that objects are split or divided– or in Harman’s parlance, that they “withdraw” –because no object actualizes all possible points within its phase space. In this connection, O1 refers to an actualized point within a phase space that the object currently occupies.

I think that this is an excellent place to start, but there are a few problems with the borrowing of these analogies from statistical mechanics. The first is these descriptors are used to describe very specific things, “closed systems”. In order for Levi to apply such a thought to his idea that everything is an object, EVERYTHING would have to be a closed system. My passing thought of my grandmother and a combustion engine would BOTH have to be a closed system, each with its own phase space and attractors. Under current understanding such a position would be more than pure invention, it would be, I think, wild analogy. Does the monetary policy of Brazil, and my dog scratching at a tick each have a “phase space”? Does “the flying spaghetti monster“? I suspect that Levi is conflating two things: one, the Idealist oriented notion of whether something is the “same” because we perceive it to be the same, giving it an idenity (something implicitly imported into Harmanism from Husserl), and the very specific energy and informational designations that cause us to regard something as a “system”.

But I do not think that this conflation is unimportant or unhelpful. There does seem to be something interesting about putting these two things into one box “identity” and “phase space”. From my perspective what is compelling comes from Spinoza’s view that a thing is a thing, and remains a certain thing due to a certain ration of motion and rest that persists over time. I think that some rough, but perhaps still very substantive comparisons can be made between this notion and the informational and energy requirements to regard something as having a “phase space”. The notion of “closure” is somewhat missing (a part of which that imports from his Idealist, Lacanian heritage). What makes things “closed”? Is it our perception of them as closed, the subjective boundary that we drawn around them, seeing them as we do, or is it some essential “phase space” and “attractor” that forces them to have a ghost-life beneath our view? This notion of closure is an important one, and the way that Levi plays with both the psychological/perceptual sense of the word and the scientific sense is problematic.

Because this is problematic ground I have been and would like to tread, this analogy to phase space is something worth paying attention to. And while I find difficult (or unhelpful) the notion that “the twinkle in her eye” is a closed system, and would like to treat closed systems as very specific things that can be considered “closed” because such an analysis yields valuable information about them (and not because they solve our philosophical question of identity), Spinoza’s definitional idea of what a body is makes the comparison between individuals and such spaces appealing. I have argued elsewhere that the closure of objects is best seen as “Semiotic” that is, making differences that make “the” difference rather than simply “a” difference: The “ens reale” and the “ens rationalis”: Spelling Out Differences, The Necessary Intersections of the Human Body: Spinoza and Conjoined Semiosis: A “Nerve Language” of Bodies. In each I take up the consequences of Spinoza’s definition of a body that I have referred to here:

Definition: When a number of bodies of the same or different magnitude form close contact with one another through the pressure of other bodies upon them, or if they are moving at the same or different rates of speed so as to preserve an unvarying relation of movement among themselves, these bodies are said to be united with one another and all together to form one body or individual thing, which is distinguished from other things through this union of bodies. E2p13a2d

What is key in our consideration is, I believe, the notion of communication, that the parts communicate their motions to each other (this can be found in the Latin phrase ut motus suos invicem certa quadam ratione communicent, translated by Curley as “that they communicate their motion to each other in a fixed manner”). This idea of communication is an important one because it opens up the “informational” dimension of what makes up a closure. What makes up a thing so as to be an “individual” is not only its material existence, but also its energy (motion/rest) AND its information (!), its communications. And yes, I do think that there are reasons to speak of the differences that make “a” difference in the world, and differences that make “the” difference (internal to a system or a taken to be recursive relationship).

But this is the thing that I think that Levi is missing, and missing rather dramatically, in his question to make objects retreat from all their relations (and gain some sort of affinity to Harman’s Idealism). Although it pays to treat objects as separate from others, because their “phase space” is informational phase space (if we even grant the more wild aspects of the analogy from Science), and as such there is no reason to suppose that such a space of relations is closed off from the rest of the universe, or composes a difference that makes NO difference to other things, other systems, other phase spaces (Levi Uses Greek Fonts Nicely, but…). In fact, such a phase space, I would suggest, is necessarily understood to be permeated (and interactive) at several levels. I think I would deny that there is ANY system that is completely closed (that although it pays to treat them as closed, they never are entirely closed at all). This is the case in terms of scale (smaller component events can have consequences both on larger component scales, and thus across boundaries that would otherwise define the system), and also in term of the boundary itself. A political population of citizens can and will intersect with a population of disease, metallic elements in a machine will be effected by magnetic fields, etc., etc, etc. IF there is going to be a “phase space” analogy of the possible distribution of material elements in any “object” it is going to be a phase space that is so complex and interwoven with others (amenable to other vectored descriptions) that the ultimate solution of the “identity” problem in philosophy will never be found. Someone like Levi would like to simply deposit the identity of objects over time in such a system space, really for almost aesthetic reasons (the desire to cross out the “O” in objects), without significantly considering what a “phase space” is and what such a reality of objects would mean for identity itself. It seems that far from making objects have a “ghost” existence outside their manifestations, an existence which would make no difference to other objects, it seems to be much the opposite. Indeed objects may be described as specific manifestations of matter, energy and information that express the possibilities of their distribution, but such a phase space actually connects them to all other objects and all other phase spaces, and has a determined effect upon them.

(A sidenote: There is the additional problem from Levi whose objects are forever in retreat that if indeed each object has a phase space, a mathematical description of such a space – using the statistical mechanics from which the analogy is derived – itself becomes an “effect” of the space itself. That is, far from being in retreat, such a space is not only expressing itself in the “object” that it underwrites, but also it is expressing itself in the mathematics, and the mathematician, that is describing it. It does not compose a difference that makes no difference, as itself has expressive properties. And one has to ask, does a “phase space” constitute an “object” as well, and have its own phase space and attractors – this is an interestng question?)

Much as in Spinoza view in which essences are expressed modally, but also remain somehow latently immanent to any one manifestation, the information space within expressions is actually that which connects things to all other things, and to take it to be in continual retreat is, I believe, a fundamental mischaracterization. If anything such a space is what, in Deleuzian fashion can be called a “distaff” space, an information space out of which all things can be and are woven. It is ultimately a space intersected with all other spaces, undermining just what the Idealist notion of “objecthood” is (a notion founded upon Brentano’s Intentionality Thesis and Descartes opticality of consciousness). At the very least, and in the most obvious fashion, because entropy is defined in statistical mechanics as the tendency of a system to pass through all the phrase space that constitutes it, an “object”, what Levi wants to call O1, by virtue of its supposed Ø phase space status, could pass into a state of extreme element distribution, all of the atoms that might constitute it floating in an entropy soup O2, and still be regarded as the same object Ø (beyond any common sense of identity). A tornado passed into mere breezes. This is somthing that might only be meaningful to say of one thing, Spinoza’s Substance. I hope to post on information, Stonier and Spinoza soon.

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The Fantasm of the Point: Vico, Plotinus, Campanella and even Badiou

(ca. 204-270 AD) 

To return to the diagram of my last post on Plotinus I want to think along with a confluence of ideas that condense upon the very center of it, the infintesmal locus of “matter” which exists merely as a private, yet also which alternately can be considered as a radiating center (under a different analogy).

The direction I want to go in this is a rumination that first starts from Badiouian notion that Being is not of the One, or “the One is not,” and that mathematics in a sense speaks Being,  pronouncing what is expressible of being-qua-being. The principle that the non-numerical One is beyond Being is of course one that Plotinus holds at the pinacle of his Ontology, for Being starts with the varigated particularization of the Nous. It is there that the predication of Being takes hold. The way that Plotinus tells it, the Nous is produced by the plentitude/emptiness of The One, and necessarily breaks it apart into a kind of representation which divides it into parts. The reason that Plotinus gives for this division into likenesses is interesting. It is that the Nous struggles with the fact that it has no control over that upon which it ultimately depends, a control which expresses itself in the desire to preserve:

The hypostasis of the Intellect [Nous] cannot maintain its vision of the One in primal unity, but “being being unable to preserve the power which it was procuring, it broke it up and made the one [power] that it might bear it part by part [katà méros]” (6.7 [38] 15.20-22). In so doing, Intellect constitutes itself as an imitation of the Good, as a many-hued and varigated Good (agathòn poíkilon).

F.M. Schroeder, citing Plotinus in Form and Transformation

Now there is a great and dissatisfying danger of simply reading these particularizations as mere abstractions of an esoteric philosophy, the most gripless of metaphysics, but Plotinus’s reasoning as to why the Nous indeed breaks up the One has strong affective, phenomenological correlates. It is the very dependency of the unity of the Nous upon what lies beyond it, and inclusive of it, that generates a corresponding particularization. In drawing power from what is outside, the inside distinguishes itself. If we turn to the simple figure of a circle (for millenia a favorite of philosophers, and think in terms of systems theory, we understand that whatever system there is, it necessarily is less complex than its environment. This is to say, as all systems (the inside) depends upon a more complex outside, the very inside/outside boundary issue of dependency drives the very divisions of the inside in regard to what lies beyond it. If we allow the observations of evolutary theory, life has moved from less to more complex, and with this increase of internal divisions (differences that make differences) it has relatively gained a greater role in the preservation of the power upon which it depends (and, notably, which it is also an expression). Plotinus’s story of the Nous serves as a metaphysical directionality which prescribes how any person (organism) might orient themselves to conditions which are beyond it, like the Nous with totalizes these relations, the move is towards a complexification of differences that make differences.

For Plotinus, this process of particularization comes from what he calls “beholding” or “witnessing”. Whereas the first particularization beholds the One/the Expressed, those of Soul and Sensation are even more narrow in what they behold, all the way down to matter, which simply exists as a non-existent privation. A speck of darkness.

A Retreat to Vico’s Conception of Mathematics: the ficta of points (1668 – 1744)

I find this speck of nothingness interesting because its very non-divisibilty division reflects something of mathematics, the way in which points or numbers are non-existent distinctions that operate as a kind of limit. What I have in mind is Giambattista Vico’s interpretation of mathematics as the most divine of human acts, because in the invention of the point and the unit human beings act just a God did, creating something out of nothing in imitation of divinity, scientia humana divinae sit imitatrix. For Vico, a forerunner to some themes found in Kant, human beings cannot truly know things that they have not created. Only God truly knows what is created. The reason why human beings can have perfect knowledge of mathematics is that its creation is wholely their own. In a sense, mathematics operates “within” the circle of human articulation.

To quote some Vico, and then a commentator, to give perspective on his position:

…man defines the names themselves, and on the model of God with no underlying thing he creates (creat) the point, line and surface as if from nothing, as if they were things…to establish (condidit) for himself a certain world of forms and numbers, which he embraces within himself: and by producing, shortening, or composing lines, by adding, substracting, or reckoning numbers, he effects infinite works because he knows infinite truths within himself

But the point of the human imagination is not the point we draw with a pencil: “the point, when you draw it, is not a point: the one, when you multiply it, is no longer fully one.”

“man, containing within himself an imaginary world of lines and numbers, operates in it with his abstractions, just as God does in the universe with reality.”

With something of Plotinus’s reasoning, the very imaginary abstraction that human beings creates is a coping mechanism for that which lies beyond them and upon which they depend. Here Robert Miner provides a good overview of Vico’s approach to the knowing of human understanding:

Abstraction is the mind’s way of coping with its estrangement from things. Because he cannot possess ‘the elementa rerum by which things themselves exist with certainty,’ he resorts to the fabrication (confingere) of elementa verborum, elements which, despite their unreality, are able to ‘stimulate ideas with no controversy.'”

Vico has described human truth as a factum that is arrived at through a synthesis of elements that are only partially grasped, because they exist outside the mind which grasps them. If the human mind is essentially outside the elementa rerum, how does it manage to grasp even their outside edges? Vico proceeds to answer this question: “God knows everything, because he contains within himself the elements from which all things are composed; man seeks to know these elements by a process of dividing (dividendo).”

What is the relation of “dividing” to making? Is dividendo creative or destructive? Vico’s answer is “both.” De antiquissima 1.2 begins with an homage to the fecundity of dissection. The “anatomy of nature’s works” gives birth to a range of human scientiae. It does so by inventing their objects. One can divide man into body and spirit. From body, human science has “picked out (excerpsit) or, as men say, abstracted figure and motion, and from these, as well as from all other things, it has extracted (extulit) being and unity.” The objects obtained through abstraction give rise to the human scientiae metaphysics (whose proper object is ens), arithmetic (unum), geometry (figura), mechanics (motus from the edge), physics (motion from the center), medicine (corpus), logic (ratio), and ethics (voluntas).

The fecundity of dissection comes at a cost. Man creates the human scientiae by fragmenting, and therefore destroying, the whole…The entities created by abstraction – being, unity, figure, motion, shape, intellect, will – are “one thing in God, in whom they are one, and another thing in man, in whom they are divided.” Ripped from the whole in which they have life, humanly obtained elements are disiecta membra. “In God they live, in man they perish.” Our efforts to understand nature by cutting it up supplies us with theories rather than works: “in nobis sunt ratiocina, in Deo sunt opera.” All that man acquires through dividing the whole, is like man himself, nihil prae Deo; all finite and created beings are nothing but disposita entis infiniti ac aeterni. Etymology confirms the connection between division and diminution: Vico asserts that minuere means both “to lessen” and “to separate.”

The limitations of abstraction ensure that we have access only to the extrema of the elementa rerum. In what is likely to be an illusion to Lucretius, Vico declares that when man starts to investigate the nature of things (naturam rerum vestigabundus), he finds that “he does not have within himself the elements from which composite things exist.” This lack (brevitas) is not a morally neutral feature of the human condition, but a “vice of the mind” (mentis vicium). It is an effect of fallenness, a decline from a primordeal state in which mind and nature where integrated. (Vico uses nefas to characterize physicists who think they can provide real defintions of things.) Man responds to this condition by turning the mentis vicium to good use, by performing an operation that relies solely upon the mind and bypasses, as it were, the material world. “By abstraction, as they say, he fabricates (configit) two things for himself: the point that can be drawn and the unit that can be multiplied.” The association of abstractio and configere suggests that abstraction is creative. The suggestion is confirmed in the Prima Riposta, where Vico writes that mathematics [move to quotes on mathematics].

Truth in Making, Robert Miner

The Terminus Point of Nonbeing: Campanella (1568 – 1639 )

 

There is another evocative figure of radiating being, that which Campanella uses to characterize how each thing is but a point from which non-Being radiates, a kind of photographic negative of Plotinus’s conception:

 What we are concerned with is something that has an actual bearing on the existential order [not “relative nothingnesss” (nihilum secundum quid), the essence of a thing prior to existence], i.e., the composition of an infinite nonbeing with a finite being in existing realities. This is the point at issue, and this Campanella tries to illustrate by means of an analogy. Just as we can conceive a line stretching from the center of the earth beyond the circumfrence of the sky in infinitum, so, he says, man, like any other creature, is but a little dot where infinite nonbeing is terminated. Man is in effect the negation of an infinite number of other things and of God himself, being surrounded, as he is, by an infinite nonbeing (Bonansea, Tommaso Campanella, citing Met, II, 6, 3, 7)

In this Campanella presents something very close to Spinoza’s letter 21 claim that “all determination is negation,” something that Hegel made quite a bit of. Only in Spinoza any particular determination/negation is not a negation of God/Substance, but rather its Substance (Campanella always heretically veering towards collapsing God and Creation into one panpsychic whole, like Spinoza, but careful to walk the line).

What I am inspired to say about these circular analogies for Being and coherence of action, with their distinct and performative inside/outside designations, is that somehow mathematics in coming out of the pure fictiveness of human creation, in inventing the Non-Being of the immaterial point, somehow grasps whole the entire matrix of radiating conceptions, and is able to map out with great fecundity the very Oneness which is beyond Being (in a Plotinian sense). Weaving out the very absence, the infintesmal (as my wife tells me, what is the decimal point which divides the infinitely large from the infinitely small, made of?), we get a glimpse of the very varigatedness that Plotinus attributes to Nous likeness taking.  The whole thing is sutured closed, or at least remotely closed, for one imagines that there are many kinds of mappings that can be woven from the nothingness of the point.

Further though, even in its appropriation of the infinite nothingness, mathematics owes Alfred Korzybski’s adage “The map is not the territory,” while keeping in mind that mapping, and map-following is itself part of the territory (one hunts through the map, as one hunts through the territory). All organisms seem to in some form follow Plotinus’s thoughts on why the Nous mirrored the One, being unable to preserve that upon which they depend. The semiotic relations that make up an organisms internal relations, and then thus relations to other organisms, are not only performances, but also are duplications (not necessarily representations), “picking out” (intelligere, to choose out) certain aspects of the world, and it is always a tension between picking out the most important, valued features, and sheer numericity, since these two are intimately related. In a certain sense, mathematics too needs to be seen as a vast material organism/organization, as material as any map, appendage to the human species.